4-Vectors

The 4-vectors are the Lorentz tensors of type (1, 0). It is important to understand that not all elements of \(M^{4}\) are four vectors! This is due to the fact that a 4-vector is a specific geometric object which under the action of a Lorentz transformation transforms in a specific way (i.e. tensorially). The elements of Minkowski space which are not Lorentz tensors do not interest us and we ignore them. One might inquire why we do not consider other groups of transformations besides the Lorentz transformations in \(M^{4}\) ; for example non-linear ones? The answer is that this is possible and can be/has been done.